Mishnah Berurah — משנה ברורה

It is valid - The Ta"z explains that Rem"a is referring to where [you know that] there is also despair [on the part of the original owner of ever getting his stolen item back], and [so] he acquired it through despair and a change in the name [of the object], because originally it was [called] "wool" and now it's [called] "string". But the Magen Avraham wrote that because the Rem"a was ambiguous, it seems that he holds that even before despair it's valid, for he acquired it through a [physical] change [brought about] by an action. And so too is it understood from the words of the Gr"a in his explanation, that the reason is because of a [physical] change [brought about] by an action... see there further. And if he stole strings and sold them to someone else before [he knew] there was despair [by the original owner], the second owner does not fulfill his obligation with these ציצית, for a change in the location [of the object] without despair, does not acquire [the object], and [therefore] it's not called "they shall make for themselves" (ie. "lahem, she'lahem" - make for themselves, from what belongs to them) [Pri Megadim]. And [regarding] if after it came into the second one's hands, the original owner despaired, see in Choshen Mishpat, Siman 353 Se'if 3, for there are varying opinions regarding this. And if [the original owners] despaired and afterwards they were sold [to a someone else], the second one acquired the ציצית, and even regarding making a blessing, it seems from the Magen Avraham in Siman 649, Se'if Kattan 2, that he could make a a blessing on it and it's not [considered] a mitzvah that came about through a sin, since he did not steal it. And this is how the Machatzit Hashekel ruled. However, the Pri Megadim over there, in the name of the Levush, is stringent regarding this. And so too, the Ta"z in Siman 25 and the Gr"a there, are stringent regarding this.